REVIEWS 329 



logarithmic computation which does not involve the log or transitions from non- 

 tabular to tabular, it is a well-known fact that the result is correct, in any event 

 to within one less significant figure than the number of places in the table. If } 

 therefore, as frequently is the case, a result must be exact to the fifth significant 

 figure, a six-place table, and no less, is a necessity. In the preparation of these 

 tables, no pains have been spared to have them accurate. Some two hundred 

 students have assisted in the reading of the proofs, and no page has been read by 

 less than ten different persons, with six-, seven-, and eight-place tables. The 

 table of circular arcs was computed by over one hundred students and checked 

 until all results agreed." A heavy ruling is used to distinguish the change in 

 leading figures when these occur in the same line, in place of the light ruling 

 which is sometimes employed, as, for instance in Chambers's " Mathematical 

 Tables." Another advantage is that differences are given at the bottom of the 

 page. On the other hand, we think that the type should have been blacker ; but 

 as the paper is fairly thick, the present light type is still easily legible. Some of 

 the trigonometrical tables, such as those on pages 38 and 39, look very crowded. 

 The preliminary instructions for the use of the tables are clear enough for the 

 most ignorant reader, and there are additional tables giving United States and 

 English measures, decimal equivalents of some of these measures, specific 

 gravities of materials, etc. 



Mr. ChappelPs book contains several innovations. He suggests a number of 

 new abbreviations — namely, Cologs, Illogs (Antilogs), Lologs (Logs of Logs), 

 Illologs (Antilologs). We find it rather difficult to trace explanations for each 

 set of tables in the preface, and wish that references had been given on the title 

 page of each such set of tables. For instance, it takes one some time to 

 ascertain what is the meaning of the figures printed red. Trigonometrical 

 functions and their logarithms are given at the end of the book. The printing 

 is very clear. 



It is unfortunate that in all these books, good tables of natural logarithms 

 are not given. In the last-named work the author says specifically that he has 

 not included such tables because these logarithms are " readily calculated by 

 means of lologs." But nevertheless even such ready calculation is often very 

 troublesome to a fatigued mind or to a busy worker. Yet natural logarithms are 

 being used more and more owing to the frequency of exponential functions in 

 statistical work, and we really wish that new books of logarithms would deal 

 with them better. We have personally actually had to fall back for these tables 

 upon such books as Dr. A. S. Percival's Practical Integration (Macmillan), where 

 there is a one-page table. 



Dr. W. P. Workman's admirable Memoranda Mathematica (Clarendon Press 

 Oxford) contains small but good logarithmic tables, including trigonometrical 

 ones ; and we cannot resist mentioning this fact because the book is so generally 

 useful for all kinds of mathematical work. 



We have received the Prospectus of an entirely new publication, the Control 

 Table of LogaritJmis (Four to Twenty-one Places) for the use of Mathematicians 

 and Calculators, Constructed by Percy Ramsey-Kent(C. & E. Layton, 56 Farringdon 

 Street, London). We are informed that this " being a control table, the calculator 

 can by its contents prove its own figures with singular ease, absolute certainty 

 and, therefore, absolute conviction to himself" ; but the methods of the table 

 are not clear. Apparently, from an accompanying letter, the author wishes to sell 

 the invention to which he refers. 



